The global set-domination number of a graph
A subset \(D\) of the vertex set \(V\) of a graph \(G\) is called global dominating set if \(D\) is a dominating set of \(G\) and of its complement \(\overline G\); see the first author [J. Math. Phys. Sci. 23, No. 5, 377- 385 (1989; Zbl 0729.05045)]. Let \(G\) be a connected graph such that \(\overline G\) is also connected. Then \(D\subset V\) is a set-dominating set if for every \(S\subset V- D\), there exists \(\varnothing\neq T\subset D\) such that the induced subgraph \(S\cup T\) is connected in \(G\). \(D\) is called global set-dominating set if the same holds for \(\overline G\) too. Among others, the authors prove that the set-dominating number equals the global set-dominating number for graphs with diameter more than 4.
scientific article; zbMATH DE number 763441